Stuck on Identity: cos(Pi/2 - x) = sin x

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Frankie

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Nov 28, 2006
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We're supposed to use addition formulas to show that:
cos(Pi/2 - x) = sin x

So far I have this for the left side:
= cos(pi/2) cos(x) + sin(pi/2) sin(x)
= 1/2(cos(pi/2 + x) + cos(pi/2 - x)) + 1/2(cos(pi/2 - x) - cos (pi/2 + x))

No here is where I'm confused. The Identities confuse the heck out of me and I don't know whether to start substituting where I can, or just factor out the problem.

Any help is appreciated.
 
½(cos(p/2 + x) + cos(p/2 – x)) + ½ (cos(p/2 – x) – cos(p/2 + x)) = 0?
 
Frankie said:
We're supposed to use addition formulas to show that:
cos(Pi/2 - x) = sin x

So far I have this for the left side:
= cos(pi/2) cos(x) + sin(pi/2) sin(x)
correct up to this point ... after this line, I have no idea what you are trying to do.
Just evalute the sum using the fact that cos(pi/2) = 0 and sin(pi/2) = 1.
ergo ...
cos(pi/2) cos(x) + sin(pi/2) sin(x) = (0)*cos(x) + (1)*sin(x) = sin(x)
you're done.

= 1/2(cos(pi/2 + x) + cos(pi/2 - x)) + 1/2(cos(pi/2 - x) - cos (pi/2 + x))

No here is where I'm confused. The Identities confuse the heck out of me and I don't know whether to start substituting where I can, or just factor out the problem.

Any help is appreciated.
Click to expand...
 
Thanks man....I'm so confused at times I'm not sure what to do. Now did you come up with cos pi/2 = 0 by actualy doing out the math?
 
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